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This is a game for two players. You will need some small-square
grid paper, a die and two felt-tip pens or highlighters. Players
take turns to roll the die, then move that number of squares in a
straight line. Move only vertically (up/down) or horizontally
(across), never diagonally. You can cross over the other player's
trails. You can trace over the top of the other player's trails.
You can cross over a single trail of your own, but can never cross
a pair of your trails (side-by-side) or trace over your own trail.
To win, you must roll the exact number needed to finish in the
target square. You can never pass through the target square. The
game ends when a player ends his/her trail in the target square, OR
when a player cannot move without breaking any of the rules.

Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?

Can't Find a Coin?

Stage: 3 Challenge Level:

Why do this problem?

In the context of trying to "fool the teacher", students may find
that it is hard to make up the results of an experiment in a
mathematically convincing way.

Possible approach

This might be a good start/end to a probability lesson, or a
regular start/end to a series of lessons. Individual students could
enter data 'live' on an interactive whiteboard, with the class
anticipating whether the 'teacher' will be fooled.

Key questions

It could lead to good discussions
- why it is hard to imitate a 'memoryless' random experiment,
- developing a series of tests to check whether data are
random.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.